Taking the Big, Big Gamble May Invovled No Risk at all
Paul Magriel, 1979
New York Times, April 12, 1979
Backgammon The second annual New England Backgammon Club Tournament, sponsored by Black and White Scotch, took place last weekend in Cambridge, Mass. Bill Robertie took top honors in a strong international field and so reinforced his standing as the best match player in the region. Ellen Jacoby Lee was the finalist; Mel Drapkin and Jim Wyckoff the semifinalists. In other sections: Roger Low overcame Charles Hesser in the consolation; Kermit Kimball defeated Lord Rennell of Rodd in the last chance; and Scott Hynek won the intermediate division.

In backgammon, a player is often faced with a choice between two plays: the “big” play, which is constructive but dangerous; and the “small” play, which is safest. An essential element of the game is the inherent tension between these two kinds of plays. Indeed, the mark of a good player is his ability to make an accurate assessment, in each case, of the risks versus the potential gains.

Roger Low, the consolation winner, demonstrated this ability in the diagrammed position, taken from his finals match against Charles Hesser. Black (Low) had already doubled and was a substantial favorite until he was hit on his 2-point by White (Hesser).

Black to play 5-1.
With the roll of 5-1, Black must now reenter on the 20-point and then consider how to play a 1. The obvious choice is 8/7, to safety his blot (exposed man) on the 8-point.

The alternative is to keep a man on the 8-point exposed to a direct 6-shot by White. Because of White’s strong 5-point home board, Black may feel that his play is too “big,” that is, unnecessarily risky. Furthermore, what would Black gain by leaving a man open? Even if White fails to roll the dreaded 6, Black is highly unlikely (only 4-4’s or 6-6’s) to cover this man next roll.

Low, however, was not deceived by this line of reasoning, and correctly chose the alternative play, bar/20, 4/3. He made an entirly different evaluation of the player’s risks and rewards. In fact, his main conclusion is remarkable — the risk (of being hit) is an illusion!

(a) bar/20, 8/7
(b) bar/20, 4/3
To see why the risk must be discounted, consider, in both cases, what happens if White rolls a 6. If Black plays safe, 8/7, and White rolls a 6, he will escape into the outfield. Because White is now far ahead in the race he will be able to redouble next roll and Black will be forced to pass. If Black plays 4/3 and is hit by a 6 as White escapes, he will, of course, also lose. In either case, if White rolls a 6 (which Black is powerless to prevent), White wins. The danger is not the hit — but the 6.

Black is powerless to prevent White from rolling a 6 — therefore he must work on the assumption that White will not roll a 6, and position himself accordingly. Keeping a spare man on the 8-point (by playing 4/3) gives Black a better builder distribution with which to attack White on the 2-point next roll. Stacking a third man on the 7-point (by playing 8/7) significantly reduces Black’s chances (by more than 50 percent) of either making the 2-point or a full prime.

XG logo
Tom Keith 2013 
Money play
White owns 2-cube
Black rolls 5-1

1296 games with VR
Checker play: 2-ply
Cube play: 3-ply Red

5-1: Game BG   Equity
1 bar/20, 8/7 W
+0.0072 x  (a)
2 bar/20, 4/3 W
−0.0942 (0.1014)  (b)

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